To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

Background: Dentin removed during root canal system instrumentation for creating adequate geometry for the canal and cleaning the canal. A new instrument had been marketed with the aim of optimum shaping of all parts of the canal system, however, no information present about the amount of dentin removal compared to conventional rotary system. This study investigated the amount of dentin removal when the canal instrumented by SAF compared with ProTaper by using high resolution computed tomography (micro CT). Materials and Methods: Twenty extracted single canalled teeth were utilized for this study; and randomly divided into 2 groups. In the first group, the root canals were prepared by using protaper rotary system till F2 and the root canal

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

Modified asphalt is considered one of the alternatives to address the problems of deficiencies in traditional asphalt concrete, as modified asphalt addresses many of the issues that appear on the pavement layers in asphalt concrete, resulting from heavy traffic and vehicles loaded with loads that exceed the design loads and the large fluctuations in the daily and seasonal temperatures of asphalt concrete. The current study examined the role of polyphosphoric acid (PPA) as a modified material for virgin asphalt when it was added in different proportions (1%, 2%, 3%, 4%) of the asphalt weight. The experimental program includes the volumetric characteristics associated with the Marshall test, the physical properties, and th

This study relates to synthesis of bentonite-supported iron/copper nanoparticles through the biosynthesis method using eucalyptus plant leaf extract, which were then named E-Fe/Cu@B-NPs. The synthesised E-Fe/Cu@B-NPs were examined by a set of experiments involving a heterogeneous Fenton-like process that removed direct blue 15 (DB15) dye from wastewater. The resultant E-Fe/Cu@B-NPs were characterised by scanning electron microscopy, Brunauer–Emmet–Teller analysis, zeta potential analysis, Fourier transform infrared spectroscopy and atomic force microscopy. The operating parameters in batch experiments were optimised using Box–Behnken design. These parameters were pH, hydrogen peroxide (H₂O₂